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Resolución de integrales/ (sqrt(2)*sin(t)^3)*(-6*sqrt(2)*sin(t)*cos(t)^2)

Integral de (sqrt(2)*sin(t)^3)*(-6*sqrt(2)*sin(t)*cos(t)^2) dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                                         
 --                                         
 3                                          
  /                                         
 |                                          
 |    ___    3         ___           2      
 |  \/ 2 *sin (t)*-6*\/ 2 *sin(t)*cos (t) dt
 |                                          
/                                           
pi                                          
--                                          
4
∫π4π32sin⁡3(t)−62sin⁡(t)cos⁡2(t) dt\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}} \sqrt{2} \sin^{3}{\left(t \right)} - 6 \sqrt{2} \sin{\left(t \right)} \cos^{2}{\left(t \right)}\, dt 
Integral((sqrt(2)*sin(t)^3)*(((-6*sqrt(2))*sin(t))*cos(t)^2), (t, pi/4, pi/3))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                              
 |                                                                           6             6           5                  5                    2       4             4       2   
 |   ___    3         ___           2                  3       3      3*t*cos (t)   3*t*sin (t)   3*sin (t)*cos(t)   3*cos (t)*sin(t)   9*t*cos (t)*sin (t)   9*t*cos (t)*sin (t)
 | \/ 2 *sin (t)*-6*\/ 2 *sin(t)*cos (t) dt = C + 2*cos (t)*sin (t) - ----------- - ----------- - ---------------- + ---------------- - ------------------- - -------------------
 |                                                                         4             4               4                  4                    4                     4         
/
∫2sin⁡3(t)−62sin⁡(t)cos⁡2(t) dt=C−3tsin⁡6(t)4−9tsin⁡4(t)cos⁡2(t)4−9tsin⁡2(t)cos⁡4(t)4−3tcos⁡6(t)4−3sin⁡5(t)cos⁡(t)4+2sin⁡3(t)cos⁡3(t)+3sin⁡(t)cos⁡5(t)4\int \sqrt{2} \sin^{3}{\left(t \right)} - 6 \sqrt{2} \sin{\left(t \right)} \cos^{2}{\left(t \right)}\, dt = C - \frac{3 t \sin^{6}{\left(t \right)}}{4} - \frac{9 t \sin^{4}{\left(t \right)} \cos^{2}{\left(t \right)}}{4} - \frac{9 t \sin^{2}{\left(t \right)} \cos^{4}{\left(t \right)}}{4} - \frac{3 t \cos^{6}{\left(t \right)}}{4} - \frac{3 \sin^{5}{\left(t \right)} \cos{\left(t \right)}}{4} + 2 \sin^{3}{\left(t \right)} \cos^{3}{\left(t \right)} + \frac{3 \sin{\left(t \right)} \cos^{5}{\left(t \right)}}{4}
Simplificar
Gráfica
0.8000.8250.8500.8750.9000.9250.9500.9751.0001.0250-2
Trazar el gráfico f(x)
Respuesta [src] 
  1   pi
- - - --
  4   16
−14−π16- \frac{1}{4} - \frac{\pi}{16} 
=
= 
  1   pi
- - - --
  4   16
−14−π16- \frac{1}{4} - \frac{\pi}{16} 
-1/4 - pi/16
Respuesta numérica [src] 
-0.446349540849362
-0.446349540849362

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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